In general, most of the time integration for numerical solution of ODEs are computed with a single formula and a fixed step-size. This type of approach can be non-optimal if the solution varies rapidly over small subsets of the integration interval and slowly over larger ones [1]}.
Using a uniform step-size, such that \(n =  is the same at every time step, the local error would vary at each time step since the error depends on the properties of \) f\( and its derivatives.A small constant step-size may help resolve regions with large variation in solution, at the expense of unnecessary computation in the region of less variability.\)
